194 MYSTICISM AND LOGIC 



been followed by the consequent, but that as long as the 

 present constitution of things endures, it always will 

 beso."^ \ 



In this sense, we shall have to give up the hope of find- 

 ing causal laws such as Mill contemplated ; any causal 

 sequence which we have observed may at any moment be 

 falsified without a falsification of any laws of the kind 

 that the more advanced sciences aim at establishing. 



In the fourth place, such laws of probable sequence, 

 though useful in daily life and in the infancy of a science, 

 tend to be displaced by quite different laws as soon as a 

 science is successful. The law of gravitation will illustrate 

 what occurs in any advanced science. > In the motions of 

 mutually gravitating bodies, there is nothing that can be 

 called a cause, and nothing that can be called an effect ; 

 there is merely a formula .J Certain differential equations 

 can be found, which hold at every instant for every 

 particle of the system, and which, given the configuration 

 and velocities at one instant, or the configurations at two 

 instants, render the configuration at any other earlier or 

 later instant theoretically calculable. That is to say, the 

 configuration at any instant is a function of that instant 

 and the configurations at two given instants. This state- 

 ment holds throughojjt physics, and not only in the special 

 case of gravitation. \ But there is nothing that could be 

 properly called ** cause " and nothing that could be 

 properly called " effect '* in such a system. .A' 



No doubt the reason why the old "law of causality " 

 has so long continued to pervade the books of philo- 

 sophers is simply that the idea of a function is unfamiliar 

 to most of them, and therefore they seek an unduly 

 simphfied statement. There is no question of repetitions 

 of the " same " cause producing the " same " effect ; it 



^ Loc. cit., 6, 



